1. Mathematical Preliminaries
- Vector Calculus: Vector algebra, scalar and vector fields, gradient, divergence, and curl operators.
- Integral Theorems: Detailed coverage and applications of Gauss’s divergence theorem, Stokes’ theorem, and Green’s theorem.
2. Electrostatics
- Electric Fields & Potentials: Coulomb’s Law, calculation of electric fields and electrostatic potential for continuous charge distributions.
- Gauss’s Law: Statement, proof, and symmetric applications (spherical, cylindrical, and planar symmetries).
- Field Equations: Poisson’s and Laplace’s equations with basic boundary value problem solutions.
- Electrostatic Energy: Energy stored in fields, systems of point charges, and a charged sphere.
3. Dielectrics & Electric Fields in Matter
- Polarization: Microscopic and macroscopic fields in dielectrics, polarization vector (\(\mathbf{P}\)), and electric displacement vector (\(\mathbf{D}\)).
- Capacitance: Capacitors filled with dielectrics, boundary conditions at dielectric interfaces, and energy density in a dielectric medium.
4. Magnetostatics
- Magnetic Forces: Biot-Savart Law, Lorentz force equation, and Ampere’s Circuital Law with applications to solenoids and toroids.
- Magnetic Vectors: Magnetic vector potential (\(\mathbf{A}\)), curl and divergence of magnetic field (\(\mathbf{B}\)).
- Magnetic Media: Diamagnetism, paramagnetism, and ferromagnetism; magnetic intensity (\(\mathbf{H}\)), magnetization (\(\mathbf{M}\)), and permeability.
5. Electromagnetic Induction & Varying Currents
- Faraday’s Law: Electromagnetic induction, Lenz’s Law, self and mutual inductance (\(\mathbf{L}\) and \(\mathbf{M}\)).
- Transient Currents: Growth and decay of currents in LR, CR, and LCR circuits.
6. Maxwell’s Equations & Electromagnetic Waves
- Maxwell’s Equations: Displacement current concept, vector formulation of Maxwell’s 4 fundamental equations in vacuum and material media.
- Wave Propagation
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